Carla bought a digital camera that cost $91.98. she also bought 2 identical memory cards and a camera case. the camera cost 6 times as much as the case. she paid $127.35, including sales tax of $6.06. what was the cost of each memory card?

Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?

News cameras take an overhead picture of a crowd at an outdoor event journalist then count the total number of people in the picture and use the sample of estimate the total number of people in the crowd this process is an example of

The bake stars picked 907 apples last weekend at a local orchard they made caramel apples and sold them in the bakery in trays of 6